The diverging overland flow model is utilized to predict surface runoff from several natural watersheds. The Lax – Wendroff scheme is used to obtain numerical solutions. This scheme is explicit, single step and second order. An analytical criterion is developed to determine time step for computation for a specified grid length in space. This criterion ensures numerical stability and convengence. The diverging geometry is specified from watershed topography. Thus the model contains one parameter which is optimized for each watershed by the Rosenbrock – Palmer optimization algorithm. The model results compare satisfactorily with runoff observations.